Ein Theorem über die Änderung des Deckungskapitals bei Sterblichkeitsvariation

Abstract

Following Lidstone’s well-known article in the Journal of the Institute of Actuaries for 1905, the author establishes, by analytical methods, sufficient conditions for variations in the mortality ratesnot giving rise to variations in the sign of the premium reserves of an endowment assurance at any time during the term of the policy. If lx is replaced, in the varied life table, by $$\tilde l_x = l_x \cdot f(x)$$ (where f(x) is a positive function which is differentiable as many times as required) there is no variation in the sign of the reserve if 0≤f(r+1)(x)·f(x) ≤ f(r)(x)·f′(x); r=0, 1, 2, 3, ... For the practical determination of such functions f(x) a method is proposed for the reduction of the number of conditions to a given finite number.